Port tuning: fb

A vented box is a Helmholtz resonator. The air in the port is a mass; the air in the box is a spring; together they resonate:

f_b = \frac{1}{2\pi\sqrt{M_{ap} C_{ab}}} = \frac{c}{2\pi}\sqrt{\frac{S_p}{V_b L_{eff}}}

At fb the port does the radiating and the cone very nearly stops moving. That is the entire point: output continues below the driver's own limits while the cone sits still, so distortion falls exactly where it would otherwise be worst.

What tuning changes

• Lower fb extends the bass but leaves the cone unsupported over a wider range, raising excursion just above tuning and steepening group delay.
• Higher fb protects the driver and tightens transient behavior, at the cost of extension and often a bump above tuning.

The cone's excursion minimum sits at fb, and moves with it. You can watch this in the excursion plot: the notch tracks the tuning field as you drag it.

Effective length, not physical length

The air just outside each end of the port moves with the air inside it, so the port behaves as though it were longer than it is. Baffle applies the standard end correction, which depends on whether each end is flanged or free. This is not a small effect (on a short, wide port the correction can be a third of the physical length) and it is why a port cut to a length from a simple formula usually tunes lower than intended.

Practical limits

Port area must be large enough to keep air velocity down, or the port whistles; see chuffing. But a larger port needs to be longer for the same tuning, and length grows quickly. At some point the port will not fit in the box, and the honest answers are a bigger box, a slot port, or a sealed design.

Below fb the port stops loading the cone entirely, which is a real hazard: see subsonic unloading.